Concealed data injection attack construction and coping method under incomplete system information

Abstract

The invention relates to a hidden data injection attack construction and coping method under incomplete system information, and the method comprises the steps: building a measurement matrix and a system model based on the physical system characteristics in an information physical system; based on the system model, establishing an attack model, and under the condition of a single unknown parameter, constructing a first hidden data injection attack relational expression for avoiding residual detection; based on the first hidden data injection attack relational expression, constructing a second hidden data injection attack relational expression capable of avoiding residual detection under the condition of multiple unknown parameters; and proposing a parameter information protection strategy based on the minimum spanning tree, and taking the first hidden data injection attack relational expression and the second hidden data injection attack relational expression as a target to obtain a core parameter needing to be protected and a minimum parameter quantity so as to cope with hidden data injection attacks under incomplete system information. Compared with the prior art, the method can assist an information physical system manager in evaluating system safety risks, identifying system key information elements and optimizing parameter protection strategies.

Description

Technical Field

[0001] The present invention relates to the field of network security, and in particular to a method for constructing and coping with hidden data injection attacks under incomplete system information. Background Art

[0002] Hidden data injection attack is a network threat that destroys data integrity by manipulating data. The attacker tampers with the measurement data in the perception or communication link, injects false or malicious data, causing the system state estimation value to deviate from the true value; at the same time, circumvents the bad data detection mechanism to maintain the attack concealment. The success of the attack is highly dependent on whether the attacker has a deep understanding of the target system estimation method and bad data detection technology, and the core lies in the attacker's understanding of the measurement matrix.

[0003] In cyber-physical systems, although attackers are partially unaware of system parameters, they can still implement malicious data manipulation based on some known parameters and the system network topology. Attackers tamper with or forge data to make it look reasonable, thereby circumventing bad data detection and manipulating state estimates, leading system managers to make wrong decisions.

[0004] Cyber-physical systems usually contain a large number of sensors, control nodes, and data transmission paths, involving complex interactions between multiple devices. By analyzing historical operating data, observing and analyzing the overall behavior of the system over a long period of time, it is possible to identify the response of the system at different time points or operating conditions. For example, attackers can exploit data inconsistencies between devices to perform hidden data injection attacks, making it impossible for system managers to detect anomalies in a timely manner. In addition, targeted attacks can be carried out on specific devices or subsystems, thereby causing global system errors and amplifying the impact of the attack.

[0005] Hidden attacks are implemented in a variety of ways and are difficult to detect. They are difficult to defend against and will damage the stable operation and security of the system. Therefore, the defender must adopt more advanced and multi-level security strategies to deal with this complex and hidden attack threat. By actively simulating potential attack scenarios, deeply analyzing the topological structure of the cyber-physical system, and mining the rules hidden in the measurement data. Studying hidden data injection attacks under incomplete system information and building defense strategies will help to implement and strengthen the network security of cyber-physical systems and promote the improvement of defense capabilities. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for constructing and coping with hidden data injection attacks under incomplete system information.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for constructing and responding to hidden data injection attacks under incomplete system information includes the following steps:

[0009] S1: Establish measurement matrix and system model based on the physical system characteristics in cyber-physical system;

[0010] S2: Based on the system model, an attack model is established, and the first hidden data injection attack relational formula for avoiding residual detection is constructed in the case of a single unknown parameter;

[0011] S3: Based on the first hidden data injection attack relational expression, a second hidden data injection attack relational expression that can avoid residual detection in the case of multiple unknown parameters is constructed;

[0012] S4: A parameter information protection strategy is proposed based on the minimum spanning tree. The goal is to make the first hidden data injection attack relationship and the second hidden data injection attack relationship invalid, and obtain the core parameters and the minimum parameter quantity that need to be protected to deal with hidden data injection attacks under incomplete system information.

[0013] Furthermore, in step S1, the information-physical system is composed of nodes and branches connecting the nodes, each branch has a single parameter, and the parameter of the branch determines the value of the non-zero elements in the measurement matrix H; the topological structure of the system and the order of arrangement of the elements of the measurement vector y jointly determine the position of the non-zero elements.

[0014] Furthermore, in step S1, the measurement matrix H is determined by the association matrix A between branches and nodes and the parameter value diagonal matrix D. The expression of the association matrix A between branches and nodes is:

[0015] A∈{-1,0,1} l×(n+1)

[0016] Where n+1 is the number of nodes, l is the number of branches, and the i-th row of the association matrix A is A i,· , i∈{1,…,l}, A i,· Contains only non-zero elements 1 or -1, 1 is located at the index position of the start node, and -1 is located at the index position of the end node;

[0017] The expression of the parameter value diagonal matrix D is:

[0018]

[0019] In the formula, the matrix E ii Only the i-th diagonal element is 1, the rest are 0, and the diagonal elements of D are D i , i∈{1,…,l},D i The corresponding element value depends on the parameter value b i ;

[0020] Select the first node as the reference node, and the calculation expression of the measurement matrix H is:

[0021]

[0022] The rank of the measurement matrix H is n.

[0023] Furthermore, in step S1, the expression of the cyber-physical system is:

[0024] y=Hx+z

[0025] In the formula, is the measurement value vector, is the system state variable vector, is the measurement matrix, is the system noise, usually a random variable vector The realized value of Σ is the noise covariance matrix.

[0026] Furthermore, in step S1, the calculation expression of minimizing the estimated residual of the system model by weighted least squares estimation method is:

[0027]

[0028] In the formula, is the estimated value of the system state; is a diagonal matrix, whose diagonal elements are preset weights, and the preset weights are the inverse of the noise variance, and the estimated residual r is obtained: The expression for the estimated residual is:

[0029]

[0030] By comparing the estimated residuals with a preset threshold Determine whether the system is running normally.

[0031] Furthermore, in step S2, the attack model is specifically:

[0032] Suppose the set of unknown parameter branches is ε is the set of all branches; the parameter diagonal matrix of the actual system branch is The parameter matrices D and D′ known to the attacker satisfy the relationship:

[0033]

[0034] In the formula, For actual i The branch line parameters are known to the attacker i The deviation of the branch line parameters, the actual measurement matrix H′ is obtained as:

[0035]

[0036] The hidden data injection attack model with unknown parameters is:

[0037] y a =H′x+z+a

[0038] K′y a ≠K′y

[0039] r′(y)=r′(y a )

[0040] Where a is the attack injection vector, K′=(H′ T WH′) -1 H′ T W,K′y a and K′y are estimated values ​​calculated based on the actual measurement matrix H′; That is, r′ is the actual residual function of the system.

[0041] Furthermore, in step S2, the construction process of the first hidden data injection attack relational formula is:

[0042] Assume that the input of functions f:ε→{1,…,n+1} and t:ε→{1,…,n+1} are branches, and the outputs are the starting node and the ending node of the branch respectively. When the attacker only targets a single branch e k When the parameters of are unknown, let ε U ={e k}, k∈{1,…,l}, f(e k )≠1 and t(e k )≠1, for all non-zero vectors If it satisfies:

[0043]

[0044] That is, the f(e k )-1 element is equal to the t(e k )-1 element, then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′;

[0045] When f(e k )=1or t(e k )=1, for all non-zero vectors If it satisfies:

[0046]

[0047] Then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′.

[0048] Furthermore, in step S3, in the case of multiple unknown parameters, the attacker has a branch set of system parameters ε U Unknown, and satisfies |ε U |>1, set f(e)≠1 and t(e)≠1, for all non-zero vectors If its right satisfy:

[0049] c f(e)-1 =c t(e)-1

[0050] That is, the f(e)-1th element of vector c is equal to the t(e)-1th element, then the attack vector a=Hc is a hidden data injection attack under H′; let When f(e) = 1 or t(e) = 1, for all non-zero vectors If its right satisfy:

[0051] c f(e)-1 =0, ift(e)=1

[0052] c f(e)-1 =0,iff(e)=1

[0053] c t(e)-1 =c f(e)-1 , iff(e)≠1andt(e)≠1

[0054] Then the attack vector a=Hc is a hidden data injection attack under H′;

[0055] Let function b:ε→{1,…,l} be the mapping between branches and branch indices, with input as branch and return as branch index. The element a in attack vector a n+1+b(e) and a n+1+l+b(e) satisfy:

[0056]

[0057] Represents the set ε U The measurement value of any branch e in the .

[0058] Further, step S4 is specifically as follows: constructing a minimum spanning tree model using a graph theory method, generating a minimum spanning tree using an equal weight condition or a proportional condition, the starting point of the minimum spanning tree is a reference node, and the node is expanded by gradually increasing the index method. For the node set and a branch set ε consisting of an undirected graph, if the subgraph yes If there is no hidden non-zero attack vector in the spanning tree, then there is no hidden non-zero attack vector.

[0059] Further, in step S4, when the sub-graph yes When the spanning tree is , there is a path connecting any two nodes, and the reference node can be connected to the other nodes through a path. Any branch e on the path satisfies:

[0060] c f(e)-1 =0, ift(e)=1

[0061] c f(e)-1 =0,iff(e)=1

[0062] c t(e)-1 =c f(e)-1 =0,iff(e)≠1andt(e)≠1

[0063] c f(e)-1 is the f(e)th vector c k )-1 element, c t(e)-1 is the t(e k )-1 element; then c=0, there is no non-zero vector Satisfy S2 or S3 conditions to deal with hidden data injection attacks under incomplete system information.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1) The present invention proposes the feasibility of an attacker constructing a hidden attack when a single or multiple parameters of the system are unknown. By establishing a system measurement matrix, modeling the cyber-physical system, and establishing an attack vector, it is proved that the attack is still valid when a single or multiple parameters of the system are unknown. At the same time, in order to resist the hidden data injection attack, the present invention uses a minimum spanning tree to construct the core parameters that need to be protected, effectively protecting the system security.

[0066] 2) The present invention assists cyber-physical system managers in assessing system security risks, identifying key information elements of the system, optimizing parameter protection strategies, effectively responding to network threats, and ensuring cyber-physical system network security. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flowchart of a method for constructing a hidden data injection attack under incomplete system information in an embodiment of the present invention is shown.

[0068] Figure 2 A schematic diagram of nodes and branches in the measurement matrix H in an embodiment of the present invention is shown.

[0069] Figure 3The embodiment of the present invention demonstrates the effect of improving the system detection probability in a power system environment when an attacker faces different unknown single-branch parameters.

[0070] Figure 4 The probability of hidden attacks when the attacker faces a branch with unknown random parameters in an embodiment of the present invention is demonstrated.

[0071] Figure 5 The invention describes a minimum spanning tree example constructed in a power system environment according to an embodiment of the invention. DETAILED DESCRIPTION

[0072] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0073] Example 1

[0074] The present invention is a method for injecting hidden data and dealing with it under incomplete system information. Figure 1 As shown, the following steps are included:

[0075] S1: Establish measurement matrix and system model based on the physical system characteristics in cyber-physical system;

[0076] The measurement matrix H is modeled as:

[0077] like Figure 2 As shown in the figure, the system consists of nodes and branches connecting the nodes. Each branch has a single parameter, and the branch parameter determines the value of the non-zero element in the measurement matrix H; the topological structure of the system and the order of the elements of the measurement vector y jointly determine the position of the non-zero element. Suppose the number of nodes in the system is n+1, the number of branches is l; the set of all branches is ε={e1,…,e l}; branch e k The specific parameter value is b k , k∈{1,…,l}; the association matrix between branches and nodes is A∈{-1,0,1} l×(n+1) ; The i-th row of matrix A is A i,· , i∈{1,…,l}, A i,· It only contains non-zero elements 1 or -1, 1 is located at the index position of the starting node, and -1 is located at the index position of the ending node; the parameter value diagonal matrix is Where matrix E ii Only the i-th diagonal element is 1, and the rest are 0; the diagonal elements of matrix D are D i , i∈{1,…,l},D i The corresponding element value depends on the parameter value b i; The inputs of functions f:ε→{1,…,n+1} and t:ε→{1,…,n+1} are branches, and the outputs are the starting node and the ending node of the branch respectively.

[0078] In order to simplify the mathematical model and calculation process and make the analysis more efficient and reliable, the first node is selected as the reference node, and the first column of the measurement matrix is ​​removed to obtain the measurement matrix H. The calculation expression is:

[0079]

[0080] The rank of the measurement matrix H is n.

[0081] The expression of the information-physical system model is:

[0082] y=Hx+z

[0083] In the formula, is the measurement value vector; is the system state variable vector; is the measurement matrix; is the system noise, usually a random variable vector The realized value of ∑ is the noise covariance matrix.

[0084] In the system, it is usually necessary to estimate the value of the state variable x based on the measured value y, and use the weighted least squares estimation method to minimize the estimated residual, which is expressed as:

[0085]

[0086] In the formula, is the estimated value of the system state; is a diagonal matrix whose diagonal elements are preset weights, usually the inverse of the noise variance. The estimated residual r is: Its expression is:

[0087]

[0088] System managers usually compare the estimated residual r with a preset threshold to determine whether the system is running normally.

[0089] S2: Based on the system model, an attack model is established, and the first hidden data injection attack relational formula for avoiding residual detection is constructed in the case of a single unknown parameter;

[0090] Suppose the set of unknown parameter branches is The parameter diagonal matrix of the actual system branch is The parameter matrices D and D′ known to the attacker satisfy the relationship:

[0091]

[0092] In the formula, For actual i The branch line parameters are known to the attacker i The deviation of branch line parameters. Therefore, the actual measurement matrix H′ of the system can be obtained as:

[0093]

[0094] The hidden data injection attack model with unknown parameters is:

[0095] y a =H′x+z+a

[0096] K′y a ≠K′y

[0097] r′(y)=r′(y a )

[0098] Where a is the attack injection vector; y = H′x + z is the original measurement, y a is the measured value after the injection attack; function r is the residual of the system estimate; after the injection attack, the estimated value Ky a is not equal to the original estimate Ky; the function r is not equal to the original estimate Ky when it takes values ​​y and y a At this point, the attack is stealth.

[0099] When the hidden data injection attack is only for a single system branch parameter, let ε U ={e k}, k∈{1,…,l}, f(e k )≠1 and t(e k )≠1, for all non-zero vectors If it satisfies:

[0100]

[0101] That is, the f(e k )-1 element is equal to the t(e k )-1 element, then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′;

[0102] When f(e k )=1or t(e k )=1, for all non-zero vectors If it satisfies:

[0103]

[0104] Then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′.

[0105] Therefore, the construction of the first hidden data injection attack relationship is achieved.

[0106] S3: Based on the first hidden data injection attack relational expression, a second hidden data injection attack relational expression that can avoid residual detection in the case of multiple unknown parameters is constructed;

[0107] The attacker implements a hidden data injection attack on the system parameter branch set ε U Unknown (i.e., multiple unknown parameters), and satisfy |ε U |=k>1. From the characteristics of H, we can see that

[0108]

[0109] In the formula, H i The calculation expression is:

[0110]

[0111] Therefore, the actual measurement matrix

[0112] set up f(e)≠1 and t(e)≠1, for all non-zero vectors If its right satisfy:

[0113] c f(e)-1 =c t(e)-1

[0114] That is, when the f(e)-1th element of vector c is equal to the t(e)-1th element, then:

[0115] [h i ] ·,2,…,n+1 c=0

[0116]

[0117] therefore:

[0118] r′(y a )=r′(y+a)=r′(y+Hc)=r′(y+H′c)=r′(y)

[0119] K′y a =K′(y+Hc)=K′(y+H′c)=K′y+c≠K′y

[0120] Then the attack vector a=Hc is a hidden data injection attack under H′.

[0121] set up f(e) = 1 or t(e) = 1. For all non-zero vectors If its right satisfy:

[0122] c f(e)-1 =0, ift(e)=1

[0123] c t(e)-1 =0,iff(e)=1

[0124] c t(e)-1 =c f(e)-1 , iff(e)≠1andt(e)≠1

[0125] but:

[0126] [H i ] ·,2,…,n+1 c=0

[0127]

[0128] therefore:

[0129] r′(y a )=r′(y+a)=r′(y+Hc)=r′(y+H′c)=r′(y)

[0130] K′y a =K′(y+Hc)=K′(y+H′c)=K′y+c≠K′y

[0131] Then the attack vector a=Hc is a hidden data injection attack under H′.

[0132] Element a in attack vector a n+1+b(e) and a n+1+l+b(e) Unpaired set ε U The measured value of any branch e in causes interference, that is:

[0133]

[0134] The same conclusion is drawn as S2, that is, the attacker can still construct the second hidden data injection attack equation when multiple parameters are unknown.

[0135] S4: A parameter information protection strategy is proposed based on the minimum spanning tree. The goal is to make the first hidden data injection attack formula and the second hidden data injection attack formula invalid, obtain the core parameters and the minimum parameter quantity that need to be protected, and realize the hidden data injection response under incomplete system information.

[0136] set up For the node set An undirected graph consisting of a branch set ε, the association matrix between branches and nodes is A. yes If the spanning tree is , there is a path connecting any two nodes, thus ensuring that the reference node can be connected to the remaining nodes through a path, and any branch e on the path satisfies:

[0137] c f(e)-1 =0, ift(e)=1

[0138] c f(e)-1 =0,iff(e)=1

[0139] c t(e)-1 =c f(e)-1 =0,iff(e)≠1andt(e)≠1

[0140] Therefore, we can know that: yes If the spanning tree of is , then c=0, so there is no non-zero vector Satisfy S2 or S3 conditions. Therefore, the minimum spanning tree is selected to construct the parameter information protection strategy, the minimum spanning tree model is constructed using the graph theory method, and the minimum spanning tree is generated using the equal weight condition or the proportional condition. The starting point of the minimum spanning tree is the reference node, and the node is expanded by gradually increasing the index method.

[0141] This embodiment is based on the IEEE power system environment, and the parameters and topology are derived from MATPOWER. The specific implementation process is as follows:

[0142] Define the relationship between the system state variable vector x and the measured value y as y = Hx + z, where the estimated value of x is The attack is constructed as a = Hc. Given a system with n+1 nodes and l branches, the set of all branches is ε = {e1,…,e k}; branch e k The specific parameter value is the impedance value b k , k∈{1,…,l}; the association matrix between branches and nodes is A; the diagonal matrix of parameter values ​​is D.

[0143] For the case where a single parameter is unknown, a branch in the system is selected to adjust the parameter value, simulating an attacker to carry out a hidden data injection attack. Attention is paid to the difference in detection probability when parameters of different branches are unknown, and the attack detection probabilities under known and unknown single parameters are compared.

[0144] Based on the IEEE 30-node test system (including 41 branches), the injection error c is generated by multivariate uniform distribution. Assume that the covariance matrix of the noise is ∑ = σ 2 I, σ=3; alarm threshold Ensure that the false positive probability is 0.05; each branch e i , the parameter changes of i∈{1,…,41} are:

[0145] ΔD i =αD i

[0146] Randomly generate 20×41 attacks.

[0147] like Figure 3 As shown in the figure, the detection probability increases when the attacker faces different single-branch parameter unknowns. The experimental results show that there is an upper limit to the increase in detection probability, and the single-branch parameter unknown has limited defense capabilities against hidden data injection attacks. If the node injected by the attack is connected to the unknown parameter node, the detection probability will increase accordingly. However, if the estimated state deviates significantly from the normal value, the manager may easily detect the system anomaly.

[0148] Select multiple branches in the system and adjust the parameter values ​​to simulate the attacker's hidden data injection attack. For the case where multiple parameters are unknown, it is intuitively believed that as the number of unknown branch parameters increases, the probability of successfully constructing a hidden data injection attack will decrease.

[0149] In this embodiment, the ratio of the number of unknown parameters to the total number of parameters in the system is used as the x-axis, and the branch index of the unknown parameters is randomly generated. The experiment is repeated 1000 times to estimate the probability of hidden attacks. Figure 4 As shown in the figure, when the number of unknown parameters is less than 40% of the total, hidden attacks are almost inevitable; as the number of unknown parameters increases, the probability of hidden attacks gradually decreases until all branch parameters are unknown, the probability drops to zero. In addition, the experiment also pointed out that when the system scale increases, in order to maintain the same level of hidden attack protection, the proportion of branches with unknown parameters increases accordingly. This shows that in large systems, system managers need to change a higher proportion of branch parameters to achieve effective and secure protection.

[0150] A graph theory method is used to construct a spanning tree model, design countermeasures for hidden attacks, and explore sufficient conditions that can effectively mitigate such attacks.

[0151] like Figure 5 As shown in Figure 1, the minimum spanning tree generated when all branch weights are the same in the power system environment, the branches of the tree are marked in red. This tree starts from the reference node and gradually increases the index and expands the node.

[0152] Table 1 lists the number of branches contained in the minimum spanning tree and its percentage of the total number of branches in the entire system under equal weight conditions. The data shows that in order to significantly improve the defense capability against hidden data injection attacks, system administrators need at least 62% to 72% of the branches to construct the minimum spanning tree.

[0153] Table 1

[0154] Test system Minimum number of branches in a spanning tree Proportion IEEE 14-Bus System 13 0.65 IEEE 30-Bus System 29 0.707 IEEE 57-Bus System 56 0.7 IEEE 118-Bus System 117 0.629 IEEE 300-Bus System 299 0.7275

[0155] According to the branch index in the MATPOWER test case data file, sort the measurement vector y and select the node with index 1 as the reference node. Assume that the weight of the branch satisfies the function w: e k The weight of the branch and D k Proportional to:

[0156] w(e k )∝D k

[0157] Table 2 lists the number of branches contained in the minimum spanning tree under proportional conditions and their percentage of the total number of branches in the entire system. It can be found that the proportion of the equal weight case is equal to the proportion of the weight case that satisfies the above formula. This conclusion still holds true even when the branch weights are randomly assigned.

[0158] Table 2

[0159] Test system Minimum number of branches in a spanning tree Proportion IEEE 14-Bus System 13 0.65 IEEE 30-Bus System 29 0.707 IEEE 57-Bus System 56 0.7 IEEE 118-Bus System 117 0.629 IEEE 300-Bus System 299 0.7275

[0160] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for constructing and responding to hidden data injection attacks under incomplete system information, characterized in that: The following steps are involved: S1: Establish measurement matrix and system model based on the physical system characteristics in cyber-physical system; S2: Based on the system model, an attack model is established, and the first hidden data injection attack relational formula for avoiding residual detection is constructed in the case of a single unknown parameter; S3: Based on the first hidden data injection attack relational expression, a second hidden data injection attack relational expression that can avoid residual detection in the case of multiple unknown parameters is constructed; S4: A parameter information protection strategy is proposed based on the minimum spanning tree. The goal is to make the first hidden data injection attack relationship and the second hidden data injection attack relationship invalid, and obtain the core parameters and the minimum parameter quantity that need to be protected to deal with hidden data injection attacks under incomplete system information.

2. According to the method of claim 1, the method is characterized in that: In step S1, the information-physical system is composed of nodes and branches connecting the nodes, each branch has a single parameter, and the parameter of the branch determines the value of the non-zero elements in the measurement matrix H; the topological structure of the system and the order of arrangement of the elements of the measurement vector y jointly determine the position of the non-zero elements.

3. According to claim 2, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S1, the measurement matrix H is determined by the association matrix A between branches and nodes and the parameter value diagonal matrix D. The expression of the association matrix A between branches and nodes is: A∈{-1,0,1} l×(n+1) Where n+1 is the number of nodes, l is the number of branches, and the i-th row of the association matrix A is A i,· , i∈{1,…,l}, A i,· Contains only non-zero elements 1 or -1, 1 is located at the index position of the start node, and -1 is located at the index position of the end node; The expression of the parameter value diagonal matrix D is: In the formula, the matrix E ii Only the i-th diagonal element is 1, the rest are 0, and the diagonal elements of D are D i , i∈{1,…,l},D i The corresponding element value depends on the parameter value b i ; Select the first node as the reference node, and the calculation expression of the measurement matrix H is: The rank of the measurement matrix H is n.

4. According to claim 3, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S1, the expression of the cyber-physical system is: y=Hx+z In the formula, is the measurement value vector, is the system state variable vector, is the measurement matrix, is the system noise, i.e., the random variable vector The realized value of Σ is the noise covariance matrix.

5. According to claim 4, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S1, the calculation expression of minimizing the estimated residual of the system model by weighted least squares estimation method is: In the formula, is the estimated value of the system state; is a diagonal matrix whose diagonal elements are preset weights, which are the inverse of the noise variance. The expression for the estimated residual is: By comparing the estimated residuals with a preset threshold Determine whether the system is running normally.

6. According to claim 5, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S2, the attack model is specifically: Suppose the set of unknown parameter branches is ε is the set of all branches; The parameter diagonal matrix of the actual system branch is The parameter matrices D and D′ known to the attacker satisfy the relationship: In the formula, For actual i The branch line parameters are known to the attacker i The deviation of the branch line parameters, the actual measurement matrix H′ is obtained as: The hidden data injection attack model with unknown parameters is: y a =H′x+z+a K'y a ≠K′y r′(y)=r′(y a ) Where a is the attack injection vector, K′=(H′ T WH′) -1 H′ T W,K′y a and K′y are estimated values ​​calculated based on the actual measurement matrix H′; That is, r′ is the actual residual function of the system.

7. According to claim 6, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S2, the construction process of the first hidden data injection attack relational formula is: Assume that the input of functions f:ε→{1,…,n+1} and t:ε→{1,…,n+1} are branches, and the outputs are the starting node and the ending node of the branch respectively. When the attacker only targets a single branch e k When the parameters of are unknown, let ε U ={e k }, k∈{1,…,l}, f(e k )≠1 and t(e k )≠1, for all non-zero vectors If it satisfies: That is, the f(e k )-1 element is equal to the t(e k )-1 element, then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′; When f(e k )=1or t(e k )=1, for all non-zero vectors If it satisfies: Then the attack vector a=Hc is a hidden data injection attack under the actual measurement matrix H′.

8. According to claim 7, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: In step S3, in the case of multiple unknown parameters, the attacker sets the system parameter branch set ε U Unknown, and satisfies |ε U |>1, set f(e)≠1 and t(e)≠1, for all non-zero vectors If its right satisfy: c f(e)-1 =c t(e)-1 That is, the f(e)-1th element of vector c is equal to the t(e)-1th element, then the attack vector a=Hc is a hidden data injection attack under H′; let When f(e) = 1 or t(e) = 1, for all non-zero vectors If its right satisfy: c f(e)-1 =0,ift(e)=1 c f(e)-1 =0,iff(e)=1 c t(e)-1 =c f(e)-1 ,iff(e)≠1andt(e)≠1 Then the attack vector a=Hc is a hidden data injection attack under H′; Let function b:ε→{1,…,l} be the mapping between branches and branch indices, with input as branch and return as branch index. The element a in attack vector a n+1+b(e) and a n+1+l+b(e) satisfy: Represents the set ε U The measurement value of any branch e in the .

9. According to claim 3, a method for constructing and responding to hidden data injection attacks under incomplete system information is characterized in that: Step S4 is specifically as follows: construct a minimum spanning tree model using a graph theory method, generate a minimum spanning tree using an equal weight condition or a proportional condition, the starting point of the minimum spanning tree is a reference node, and expand the node by gradually increasing the index. For the node set and a branch set ε consisting of an undirected graph, if the subgraph yes If there is no hidden non-zero attack vector, then there is no hidden non-zero attack vector.

10. A method for constructing and coping with hidden data injection attacks under incomplete system information according to claim 9, characterized in that: In step S4, when the subgraph yes When the spanning tree is , there is a path connecting any two nodes, and the reference node can be connected to the other nodes through a path. Any branch e on the path satisfies: c f(e)-1 =0,ift(e)=1 c f(e)-1 =0,iff(e)=1 c t(e)-1 =c f(e)-1 =0,iff(e)≠1andt(e)≠1 c f(e)-1 is the f(e)th vector c k )-1 element, c t(e)-1 is the t(e k )-1 element; then c=0, there is no non-zero vector Satisfy S2 or S3 conditions to deal with hidden data injection attacks under incomplete system information.

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